Intermediate modular curves with infinitely many quartic points

2025/04/22 by Derickx, Maarten, Orlić, Petar
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2504.15937

Abstract

For every group \±1\⊆ Δ⊆ (\mathbb Z/N\mathbb Z)^×, there exists an intermediate modular curve X_Δ(N). In this paper we determine all curves X_Δ(N) with infinitely many points of degree 4 over \mathbb Q. To do that, we developed a method to compute possible degrees of rational morphisms from X_Δ(N) to an elliptic curve.

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• Tetragonal intermediate modular curves
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• Modular curves 𝑋₀(𝑁) of density degree 5